differential equations - What does the Error Message in DSolve really mean?

Having this ordinary non linear differential equation

$y'-x^2 (y+1)\cdot (y-2)^2= 0$ with the boundary condition

$y(4)=2$ . When trying to solve this one with Mathematica by using

DSolve[{y'[x] - x^2 (y[x] + 1) (y[x] - 2)^2 == 0, y[4] == 2}, y[x], x]

it gives an empty set of solution and returns

DSolve::bvnul: For some branches of the general solution, the given boundary conditions lead to an empty solution. >>

As we have

$y'=x^2(y+1)\cdot (y-2)^2$ which is clearly lipschitz continuous a local unique solution exists. In special

$y=2 \quad \forall x$ is a solution of the differential equation. When using NDSolveand plotting the results it looks pretty much like the constant function which solves the ode. How does it come that Mathematica says there is no solution?

I am using Mathematica 9.0.1 (Student Edition).

Comments

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